# Higgs to 4 lepton decay involving virtual photon

In Gluon gluon production of Higgs, is it possible for higgs to decay to following channels:

1. A pair of virtual photons which then decay to a pair of leptons each.

2. To an on shell Z boson and a virtual photon and then each of them decays to a pair of leptons?

I am asking this question in reference to the standard model or (higgs) effective field theory for higgs to 4 lepton channel.

Since Feynman rules feature neither a vertex $H\gamma\gamma$, nor a vertex $HZ\gamma$, what you considered requires higher-order corrections. Here is the leading-order tree diagram and the next-leading-order diagrams matching your criteria, i.e. 4 leptons in the final state, with a vertex $Z l^+l^-$ or $\gamma l^+l^-$.